What Happens When the Tension in a Musical Instrument String is Doubled?

[Sky07]

Hello, I am having a hard time solving this question. Any help is really appreciated.

1. Homework Statement
You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of mass per unit length μacross the open end of the tube. The other end of the tube is closed. To produce the musical effect you're looking for, you want the frequency of the third-harmonic standing wave on the string to be the same as the fundamental frequency for sound waves in the air column in the tube. The speed of sound waves in this air column is vs.

b)What happens to the sound produced by the instrument if the tension is changed to twice the value calculated . The tension is vsound^2μ/60?

c) For the tension calculated vsound^2μ/60, what other harmonics of the string, if any, are in resonance with standing waves in the air column?

Homework Equations

ƒn=nv/2L

The Attempt at a Solution

[/B]
B) for this part my idea is because tension is increasing the the frequency of the waves will increase as per the formula. However, I am unsure if the sound would become a higher pitch or lower pitch.
C) I am not really sure about this one.

Thank you for your help!

 

[haruspex]

The tension is vsound^2μ/60?

That's the tension before it is doubled? I get something different - please post your working. However, it is only different by a constant factor, so shouldn't change the answer to b.

the frequency of the waves will increase as per the formula. However, I am unsure if the sound would become a higher pitch or lower pitch.

You don't know whether a higher frequency is a higher or lower pitch?

What happens to the sound produced by the instrument if the tension is changed to twice the value calculated

You're not told how the instrument is to be played, but presumably the idea is to pluck the string. You need to think on this very carefully: What will happen when you do that with the original design?
What will happen when you pluck the string with twice the tension?